Bayesian Startup Phase Mean Monitoring of an Autocorrelated Process That Is Subject to Random Sized Jumps

Abstract

In this work we will provide a monitoring scheme for the mean of an autocorrelated process which can experience bidirectional jumps of random size and occurrence and has a steady state. Our interest focuses in the start up phase and short-run scenarios, where traditional SPC techniques fail to provide formal testing. Furthermore, we will provide a framework where prior information regarding the process can be employed. These will be achieved by adopting a Bayesian sequentially updated scheme that will allow inference in an online fashion. The performance of the proposed model will be compared against other methods which can be applied in similar settings. A simulation study along with a real data application from the dairy business will conclude this work. Supplemental files are available online, with technical details and the code for applying the proposed methodology in R.

Keywords:  :

• Bayesian statistical process control
• Normal mixtures
• Online inference
• Short runs